Welcome to Android Central! To expand on belodion's post: Charge up to 100%, then let it drain to 20-30% with normal usage, without charging in between. Then show us:

1. The main Settings>Battery screen.
2. The fullscreen battery graph screen (which shows Awake time and Cell Signal Strength).
3. The Screen category (to see total Screen On time).
4. The Cell Standby category, if present (to see Time Without Signal).